CHAPTER IV.

SYSTEM OF CHEMICAL EQUIVALENTS-EQUIVALENT NOTATION,

I.

THE interpretation which Berzelius had given of the law of volumes formed, as we have seen in the preceding pages, one of the foundations of his system of atomic weights and of his notation. This foundation was destroyed by the researches of Dumas, and subsequently of Mitscherlich, upon vapour densities commenced in 1827. Dumas noticed that the vapour density of mercury is sensibly equal to 100, hydrogen being taken as unity. The vapour densities of mercury and of oxygen are as 100: 16 or as 50: 8. If the atomic weights were proportional to the densities, 8 of oxygen should combine with 50 of mercury to form mercuric oxide. This is not the case; mercuric oxide is composed of 8 of oxygen and 100 of mercury, and it is the latter number which Berzelius had adopted for the atomic weight of mercury. If equal volumes of oxygen and of mercury vapour contain the same number of atoms, their densities should be in the ratio of 8 to 100, or, in other words, the density of mercury vapour

is only half what it should be. We have here evidently a well-marked exception, or, better, a manifest contradiction between the facts and the principle admitted by Berzelius. Other exceptions may be mentioned. The vapour densities of sulphur and phosphorus determined by Dumas in 1832 were found to be, in the first case, three times as great, and in the second twice as great, as those indicated by theory. Chemical considerations have caused a composition, expressed by the formulæ HS and SO,, to be attributed to sulphuretted hydrogen and sulphuric anhydride. From these formulæ the ratio between the atomic weights of sulphur, oxygen, and hydrogen is expressed by the numbers. 32:1:16, and the densities should be in the same ratio. Now, the vapour density of sulphur taken at about 560° is 96, hydrogen being taken as unity. From this density a quantity weighing 32 in the molecule of sulphuretted hydrogen would not represent an atom of sulphur, but of an atom, and the formula of sulphuretted hydrogen, expressed in conformity with the law of volumes, would be H2S, which is inadmissible.

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From the formulæ PH, and P,O,, adopted for phosphoretted hydrogen and phosphoric anhydride respectively, the relation between the atomic weights of phosphorus, hydrogen, and oxygen should be expressed by the numbers 31: 1:16. Now, the vapour density of phosphorus is equal to 2 × 31=62. If, therefore, the density of sulphur vapour is three times greater than that indicated by theory, that of phosphorus is twice as great. The case is the same with that of arsenic, from

an experiment of Mitscherlich, who also confirmed, in 1833, the results obtained by Dumas upon the vapour of mercury, sulphur, and phosphorus.

We here, therefore, meet with a serious difficulty. For its solution two courses are open to us: we must either maintain the principle of the equality of the number of atoms in equal volumes of gases or vapours, and determine to assign to mercury, sulphur, phosphorus, and arsenic atomic weights which shall conform to the vapour densities, although they are less probable, and consequently to give their compounds the formulæ Hg20, H2S, PH; or else it will become necessary to sacrifice the principle under discussion, in order to enable us to adopt the atomic weights, HgO, indicated by chemical analogies and the law of specific heats. The atomic weights of mercury, sulphur, phosphorus, and arsenic being, therefore, 200, 32, 31, 75, referred to hydrogen as unity, the preceding formulæ become. HgO, H2S, PH,, and AsH3.

It is the latter course which chemists have adopted, since they were properly unwilling to neglect more evident analogies. But the adoption of these atomic weights involves the following consequences :

1. The vapour of mercury, the density of which is only half that required by the atomic weight assigned to mercury, evidently contains half the number of atoms contained in an equal volume of hydrogen.

2. The vapour of sulphur, which at 500° is three times as dense as it should be from the atomic weight assigned to sulphur, contains, at this temperature, three times the number of atoms contained in an equal volume of hydrogen.

3. The vapours of phosphorus and arsenic, which are twice as dense as they should be from their atomic weights, evidently contain twice as many atoms as an equal volume of hydrogen.

The atomic constitution of gases or of elementary vapours is not, therefore, always the same, as Berzelius for a long time supposed. If we compare gases or elementary vapours, as far as concerns the number of atoms which they contain, to the vapour of mercury, which contains the least, we shall have the result that, if mercury vapour contains in a certain volume one atom, hydrogen, oxygen, nitrogen, chlorine, bromine, and iodine contain 2, phosphorus and arsenic contain 4, while sulphur at 500° contains 6. The relations between the number of atoms contained in equal volumes of gases or of vapours may be obtained by dividing the density of the gas or vapour by the corresponding atomic weight. We shall thus obtain the following results:

We have, therefore, to distinguish monatomic, diatomic, tetratomic, and hexatomic gases. Gmelin has already introduced into science a similar distinction, which has now become so important. At p. 54 of the first volume of the fourth edition of his treatise he gives a table analogous to the preceding, with some differences due to the different atomic weights adopted. Those used in our table are those of Berzelius (p. 62), which are now adopted for the respective elements.

With Gmelin and other chemists who soon followed his example it was different. As we have already remarked, the former maintained the proportional numbers which he designated in the first editions of his classical treatise by the erroneous term of 'Mischungsgewichte," and which he referred to hydrogen as unity, following the example of Dalton. In the fourth edition of his work he returns to the term atomic weights, but the numbers thus designated were identical with the proportional numbers or equivalents.

II.

The system of chemical equivalents and the notation derived from them gradually prevailed over the system of atomic weights and the notation of Berzelius, and are still preferred by some French chemists. It will therefore be useful to explain the principles upon which this equivalent notation rests, and particularly the arguments used by Gmelin against Berzelius in the question which forms the chief point of the discussion—

'Literally mixing weights,' instead of 'combining weights.